66. And?

How about Korea. Approximately the same near-total ban on firearms as Japan. Suicide rate 31/100,000. (10/100k higher than Japan even)

Even though they make up the lion's share of suicides AND the lion's share of gun-related deaths in the united states, our total suicide rate is 11.8/100,000 per year.

Perspective is important.

There are certainly examples of nations with tighter gun control than the US, with lower suicide rates, like the UK. Suicide is more of a cultural issue, as you pointed out, the weapon employed to accomplish it is largely irrelevant. As we can see by looking at the list of countries with the highest suicide rates, firearms are pretty incidental.